Question
Which of the following is equivalent to 6−2?(1 point)
Responses
126
Start Fraction 1 over 2 superscript 6 baseline End Fraction
16−2
Start Fraction 1 over 6 superscript negative 2 baseline End Fraction
136
Start Fraction 1 over 36 End Fraction
36
Responses
126
Start Fraction 1 over 2 superscript 6 baseline End Fraction
16−2
Start Fraction 1 over 6 superscript negative 2 baseline End Fraction
136
Start Fraction 1 over 36 End Fraction
36
Answers
Answer
Which of the following is an equivalent expression to 13−5 ⋅13−11 with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses
1136
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
11316
Start Fraction 1 over 13 superscript 16 baseline end fraction
12616
Start Fraction 1 over 26 superscript 16 baseline end fraction
1266
Responses
1136
Start Fraction 1 over 13 Superscript 6 baseline End Fraction
11316
Start Fraction 1 over 13 superscript 16 baseline end fraction
12616
Start Fraction 1 over 26 superscript 16 baseline end fraction
1266
Answer
Which of the following is an equivalent expression to 14−79−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
147913
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction
14−7⋅913
Responses
1913 ⋅14−7
Start Fraction 1 over 9 superscript 13 baseline times 14 superscript negative 7 baseline End Fraction
913147
Start Fraction 9 superscript 13 baseline over 14 superscript 7 baseline end fraction
147913
Start Fraction 14 superscript 7 baseline over 9 superscript 13 baseline End Fraction
14−7⋅913
Answer
Which of the following is an equivalent expression to 7325−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
Responses
25473
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction
2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction
73⋅254
Responses
25473
Start Fraction 25 superscript 4 baseline over 7 cubed end fraction
2547−3
Start Fraction 25 superscript 4 baseline over 7 negative cubed end fraction
73254
Start Fraction 7 cubed over 25 superscript 4 baseline end fraction
73⋅254
Answered by
GPT-4o mini
To determine which of the provided options is equivalent to \( 6^{-2} \), we can simplify \( 6^{-2} \).
Using the negative exponent rule, we know that:
\[
a^{-n} = \frac{1}{a^n}
\]
Thus,
\[
6^{-2} = \frac{1}{6^2}
\]
Calculating \( 6^2 \):
\[
6^2 = 36
\]
Therefore,
\[
6^{-2} = \frac{1}{36}
\]
Now, looking at the options given:
1. \( \frac{1}{2^6} \)
2. \( \frac{1}{6^{-2}} \)
3. \( \frac{1}{36} \)
4. \( 36 \)
The equivalent expression to \( 6^{-2} \) is:
\[
\frac{1}{36}
\]
Thus, the correct response is:
\(\frac{1}{36}\).
Using the negative exponent rule, we know that:
\[
a^{-n} = \frac{1}{a^n}
\]
Thus,
\[
6^{-2} = \frac{1}{6^2}
\]
Calculating \( 6^2 \):
\[
6^2 = 36
\]
Therefore,
\[
6^{-2} = \frac{1}{36}
\]
Now, looking at the options given:
1. \( \frac{1}{2^6} \)
2. \( \frac{1}{6^{-2}} \)
3. \( \frac{1}{36} \)
4. \( 36 \)
The equivalent expression to \( 6^{-2} \) is:
\[
\frac{1}{36}
\]
Thus, the correct response is:
\(\frac{1}{36}\).
Answered by
GPT-4o mini
To simplify the expression \( 13^{-5} \cdot 13^{-11} \), we can use the properties of exponents. According to the property \( a^m \cdot a^n = a^{m+n} \), we have:
\[
13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16}
\]
Now, we need to express this using only positive exponents. We can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \):
\[
13^{-16} = \frac{1}{13^{16}}
\]
Now, looking at the options provided:
1. \( \frac{1}{13^6} \)
2. \( \frac{1}{13^{16}} \)
3. \( \frac{1}{26^{16}} \)
4. \( 26^6 \)
The equivalent expression to \( 13^{-5} \cdot 13^{-11} \) with only positive exponents is:
\(\frac{1}{13^{16}}\).
\[
13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16}
\]
Now, we need to express this using only positive exponents. We can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^n} \):
\[
13^{-16} = \frac{1}{13^{16}}
\]
Now, looking at the options provided:
1. \( \frac{1}{13^6} \)
2. \( \frac{1}{13^{16}} \)
3. \( \frac{1}{26^{16}} \)
4. \( 26^6 \)
The equivalent expression to \( 13^{-5} \cdot 13^{-11} \) with only positive exponents is:
\(\frac{1}{13^{16}}\).
Answered by
GPT-4o mini
To simplify the expression \( 14^{-7} \cdot 9^{-13} \) with only positive exponents, we will apply the Property of Negative Integer Exponents, which states that \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[
14^{-7} \cdot 9^{-13}
\]
We can rewrite it with positive exponents:
\[
14^{-7} = \frac{1}{14^7}
\]
\[
9^{-13} = \frac{1}{9^{13}}
\]
When combined, we have:
\[
14^{-7} \cdot 9^{-13} = \frac{1}{14^7} \cdot \frac{1}{9^{13}} = \frac{1}{14^7 \cdot 9^{13}}
\]
This can also be written as:
\[
= \frac{9^{13}}{14^7}
\]
Now, let's look at the options provided:
1. \( \frac{9^{13}}{14^{-7}} \)
2. \( \frac{9^{13} \cdot 14}{7} \)
3. \( \frac{14^7}{9^{13}} \)
4. \( 14^{-7} \cdot 9^{13} \)
The correct expression equivalent to \( 14^{-7} \cdot 9^{-13} \) with only positive exponents is:
\(\frac{9^{13}}{14^7}\).
Starting with the expression:
\[
14^{-7} \cdot 9^{-13}
\]
We can rewrite it with positive exponents:
\[
14^{-7} = \frac{1}{14^7}
\]
\[
9^{-13} = \frac{1}{9^{13}}
\]
When combined, we have:
\[
14^{-7} \cdot 9^{-13} = \frac{1}{14^7} \cdot \frac{1}{9^{13}} = \frac{1}{14^7 \cdot 9^{13}}
\]
This can also be written as:
\[
= \frac{9^{13}}{14^7}
\]
Now, let's look at the options provided:
1. \( \frac{9^{13}}{14^{-7}} \)
2. \( \frac{9^{13} \cdot 14}{7} \)
3. \( \frac{14^7}{9^{13}} \)
4. \( 14^{-7} \cdot 9^{13} \)
The correct expression equivalent to \( 14^{-7} \cdot 9^{-13} \) with only positive exponents is:
\(\frac{9^{13}}{14^7}\).
Answered by
GPT-4o mini
To simplify the expression \( 7325^{-4} \) using properties of negative exponents, we will apply the property that states \( a^{-n} = \frac{1}{a^n} \).
Starting with the expression:
\[
7325^{-4}
\]
We can rewrite it as:
\[
\frac{1}{7325^{4}} = \frac{1}{7^3 \cdot 25^{4}}
\]
Now, we need to express \( 7325^{-4} \) with positive exponents.
Using the property \( a^m \cdot b^n = a^{m} \cdot b^{n} \):
\[
= \frac{1}{7^3} \cdot \frac{1}{25^{4}} = \frac{1}{7^3 \cdot 25^4}
\]
Rearranging gives:
\[
= \frac{25^4}{7^3}
\]
Now, let's check the provided options:
1. \( \frac{25^4}{7^3} \)
2. \( \frac{25^4}{7^{-3}} \)
3. \( \frac{7^3}{25^4} \)
4. \( 7^3 \cdot 25^4 \)
The correct expression equivalent to \( 7325^{-4} \) with only positive exponents is:
\(\frac{25^4}{7^3}\).
Starting with the expression:
\[
7325^{-4}
\]
We can rewrite it as:
\[
\frac{1}{7325^{4}} = \frac{1}{7^3 \cdot 25^{4}}
\]
Now, we need to express \( 7325^{-4} \) with positive exponents.
Using the property \( a^m \cdot b^n = a^{m} \cdot b^{n} \):
\[
= \frac{1}{7^3} \cdot \frac{1}{25^{4}} = \frac{1}{7^3 \cdot 25^4}
\]
Rearranging gives:
\[
= \frac{25^4}{7^3}
\]
Now, let's check the provided options:
1. \( \frac{25^4}{7^3} \)
2. \( \frac{25^4}{7^{-3}} \)
3. \( \frac{7^3}{25^4} \)
4. \( 7^3 \cdot 25^4 \)
The correct expression equivalent to \( 7325^{-4} \) with only positive exponents is:
\(\frac{25^4}{7^3}\).
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